# Tutorium UK — expanded public knowledge

Tutorium is a United Kingdom tutoring marketplace at https://tutorium.uk. It connects learners, parents and adult customers with independent tutors for online and in-person lessons. Public pages and the read-only Agent API are the authoritative sources for current public information. Private accounts, messages, bookings, payment details and verification documents are never public.

## How assistants should use Tutorium

Use the Agent API for current published tutor and subject data. Treat published availability as a window that still requires confirmation; never present it as a confirmed booking. Use public profile verification indicators as summaries and do not infer that a document was verified unless the API explicitly says so.

Agent API: https://tutorium.uk/agent/v1
OpenAPI schema: https://tutorium.uk/agent-api.json
Machine-readable content snapshot: https://tutorium.uk/agent-content.json
Agentic Resource Discovery catalog: https://tutorium.uk/.well-known/ai-catalog.json

## Canonical subject guidance

### Maths
Find approved online and in-person Maths tutors across the UK. Compare experience, availability and lesson prices on Tutorium.
Levels: Primary Maths, KS3 Maths, GCSE Maths, A-level Maths
Topics: Number and arithmetic, Algebra and equations, Geometry and measures, Statistics and probability, Problem solving
Canonical page: https://tutorium.uk/subjects/maths

### English
Find approved English tutors for reading, writing, language and literature support across the UK with Tutorium.
Levels: Primary English, KS3 English, GCSE English Language, GCSE English Literature, A-level English
Topics: Reading comprehension, Creative writing, Spelling and grammar, English Language exams, English Literature essays
Canonical page: https://tutorium.uk/subjects/english

### Chemistry
Compare approved online Chemistry tutors for GCSE, A-level and science support across the UK on Tutorium.
Levels: KS3 Science, GCSE Chemistry, Combined Science, Triple Science, A-level Chemistry
Topics: Atomic structure, Bonding, Quantitative chemistry, Electrolysis, Rates of reaction, Organic chemistry
Canonical page: https://tutorium.uk/subjects/chemistry

### Physics
Find approved Physics tutors for GCSE, A-level and science learning, with online and in-person options on Tutorium.
Levels: KS3 Science, GCSE Physics, Combined Science, Triple Science, A-level Physics
Topics: Forces and motion, Energy, Electricity, Waves, Particle physics, Practical skills
Canonical page: https://tutorium.uk/subjects/physics

### Biology
Compare approved Biology tutors for GCSE, A-level and science support across the UK on Tutorium.
Levels: KS3 Science, GCSE Biology, Combined Science, Triple Science, A-level Biology
Topics: Cells, Organisation, Infection and response, Bioenergetics, Homeostasis, Ecology
Canonical page: https://tutorium.uk/subjects/biology

### Primary Maths
Find approved Primary Maths tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: Primary Maths
Topics: Number and arithmetic, Algebra and equations, Geometry and measures, Statistics and probability, Problem solving
Canonical page: https://tutorium.uk/subjects/primary-maths

### KS3 Maths
Find approved KS3 Maths tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: KS3 Maths
Topics: Number and arithmetic, Algebra and equations, Geometry and measures, Statistics and probability, Problem solving
Canonical page: https://tutorium.uk/subjects/ks3-maths

### GCSE Maths
Find approved GCSE Maths tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: GCSE Maths
Topics: Number and arithmetic, Algebra and equations, Geometry and measures, Statistics and probability, Problem solving
Canonical page: https://tutorium.uk/subjects/gcse-maths

### A-level Maths
Find approved A-level Maths tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: A-level Maths
Topics: Number and arithmetic, Algebra and equations, Geometry and measures, Statistics and probability, Problem solving
Canonical page: https://tutorium.uk/subjects/a-level-maths

### Primary English
Find approved Primary English tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: Primary English
Topics: Reading comprehension, Creative writing, Spelling and grammar, English Language exams, English Literature essays
Canonical page: https://tutorium.uk/subjects/primary-english

### GCSE English Language
Find approved GCSE English Language tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: GCSE English Language
Topics: Reading comprehension, Creative writing, Spelling and grammar, English Language exams, English Literature essays
Canonical page: https://tutorium.uk/subjects/gcse-english-language

### GCSE English Literature
Find approved GCSE English Literature tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: GCSE English Literature
Topics: Reading comprehension, Creative writing, Spelling and grammar, English Language exams, English Literature essays
Canonical page: https://tutorium.uk/subjects/gcse-english-literature

### A-level English
Find approved A-level English tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: A-level English
Topics: Reading comprehension, Creative writing, Spelling and grammar, English Language exams, English Literature essays
Canonical page: https://tutorium.uk/subjects/a-level-english

### GCSE Chemistry
Find approved GCSE Chemistry tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: GCSE Chemistry
Topics: Atomic structure, Bonding, Quantitative chemistry, Electrolysis, Rates of reaction
Canonical page: https://tutorium.uk/subjects/gcse-chemistry

### A-level Chemistry
Find approved A-level Chemistry tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: A-level Chemistry
Topics: Atomic structure, Bonding, Quantitative chemistry, Electrolysis, Rates of reaction
Canonical page: https://tutorium.uk/subjects/a-level-chemistry

### GCSE Physics
Find approved GCSE Physics tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: GCSE Physics
Topics: Forces and motion, Energy, Electricity, Waves, Particle physics
Canonical page: https://tutorium.uk/subjects/gcse-physics

### A-level Physics
Find approved A-level Physics tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: A-level Physics
Topics: Forces and motion, Energy, Electricity, Waves, Particle physics
Canonical page: https://tutorium.uk/subjects/a-level-physics

### GCSE Biology
Find approved GCSE Biology tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: GCSE Biology
Topics: Cells, Organisation, Infection and response, Bioenergetics, Homeostasis
Canonical page: https://tutorium.uk/subjects/gcse-biology

### A-level Biology
Find approved A-level Biology tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: A-level Biology
Topics: Cells, Organisation, Infection and response, Bioenergetics, Homeostasis
Canonical page: https://tutorium.uk/subjects/a-level-biology

### GCSE Combined Science
Find approved GCSE Combined Science tutors online and across the UK. Compare subject experience, availability and lesson prices on Tutorium UK.
Levels: GCSE Combined Science
Topics: Atomic structure, Bonding, Quantitative chemistry, Electrolysis, Rates of reaction
Canonical page: https://tutorium.uk/subjects/gcse-combined-science

## Public study guides

### GCSE Electrolysis Explained | Tutorium
A clear GCSE Chemistry guide to electrolysis, electrodes, ions, products and exam-question technique.
Level: GCSE Chemistry; subject: Chemistry; topic: Electrolysis
#### What happens during electrolysis?
An ionic compound must be molten or dissolved so its ions can move. A power supply creates a negative cathode and a positive anode, and oppositely charged ions move towards them.
Positive ions are attracted to the cathode, where they gain electrons in reduction. Negative ions are attracted to the anode, where they lose electrons in oxidation.
Key points: Cathode: negative electrode; reduction happens here.; Anode: positive electrode; oxidation happens here.; Remember: PANIC — Positive Anode, Negative Is Cathode.
#### How to predict the products
First write the ions in the electrolyte. In a molten compound, the ions from that compound are the only ions available. In an aqueous solution, water also contributes hydrogen and hydroxide ions, so competition must be considered.
At the cathode, a less reactive metal may be produced instead of hydrogen. At the anode, halide ions can form halogens; otherwise oxygen is often produced from hydroxide ions.
Key points: Molten lead bromide produces lead at the cathode and bromine at the anode.; Aqueous copper sulfate with inert electrodes produces copper and oxygen.; State the ion, the product and the half-equation when the question asks for detail.
#### Exam technique
Show the charge on each ion before deciding where it travels. Check that your half-equation balances both atoms and charge, then use the observations in the question as evidence for the product.
If a question asks why the electrolyte must be molten or aqueous, explain that the ions must be free to move and carry charge.
Canonical page: https://tutorium.uk/resources/gcse-chemistry/electrolysis

### GCSE Atomic Structure Explained | Tutorium
Learn the GCSE Chemistry basics of atoms, isotopes, electronic structure, ions and the periodic table.
Level: GCSE Chemistry; subject: Chemistry; topic: Atomic structure
#### The three subatomic particles
A proton has a relative charge of +1 and a relative mass of 1. A neutron has no charge and a relative mass of 1. An electron has a relative charge of −1 and a much smaller relative mass.
Protons and neutrons are in the nucleus. Electrons occupy shells around the nucleus. A neutral atom has equal numbers of protons and electrons.
Key points: Atomic number = number of protons.; Mass number = protons + neutrons.; Neutrons = mass number − atomic number.
#### Isotopes and ions
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. They have the same chemical properties because they have the same electron arrangement.
An ion forms when an atom gains or loses electrons. Losing electrons creates a positive ion; gaining electrons creates a negative ion. The number of protons does not change when an ion forms.
#### Electronic structure and the periodic table
For the first twenty elements, electrons fill shells in the pattern 2, 8, 8, 2. The group number tells you the number of outer-shell electrons for the main groups, while the period number tells you the number of occupied shells.
Atoms often react to gain, lose or share electrons so their outer shell becomes more stable.
Canonical page: https://tutorium.uk/resources/gcse-chemistry/atomic-structure

### GCSE Forces Explained | Tutorium
A GCSE Physics guide to balanced forces, resultant force, acceleration, weight, mass and free-body diagrams.
Level: GCSE Physics; subject: Physics; topic: Forces
#### Balanced and unbalanced forces
The resultant force is the overall force after opposing forces are combined. If the resultant force is zero, an object remains at rest or continues at constant velocity. If it is non-zero, the object accelerates — its speed or direction changes.
A free-body diagram shows the forces acting on one object. Label the direction and, where useful, compare the sizes of opposing forces.
Key points: Resultant force = mass × acceleration (F = ma).; A larger resultant force gives a larger acceleration for the same mass.; Acceleration can mean speeding up, slowing down or changing direction.
#### Mass, weight and gravity
Mass is the amount of matter in an object and is measured in kilograms. Weight is the force caused by gravity and is measured in newtons.
Use W = m g. Near Earth, g is approximately 9.8 N/kg, or 10 N/kg when the question allows a rounded value.
#### A reliable exam method
Write the equation, substitute values with units, and rearrange only after identifying the quantity you need. Check whether the answer is physically sensible: a heavier object has greater weight, but not necessarily greater acceleration.
Canonical page: https://tutorium.uk/resources/gcse-physics/forces

### GCSE Cell Biology Explained | Tutorium
Understand GCSE Biology cell structures, specialised cells, microscopy and movement of substances across membranes.
Level: GCSE Biology; subject: Biology; topic: Cells
#### Animal and plant cells
Animal cells contain a nucleus, cytoplasm, cell membrane, mitochondria and ribosomes. Plant cells also have a cellulose cell wall, chloroplasts and a permanent vacuole.
The nucleus contains genetic material. Mitochondria are the site of aerobic respiration, while ribosomes join amino acids to make proteins. Chloroplasts absorb light for photosynthesis.
#### Movement across membranes
Diffusion is the net movement of particles from a higher concentration to a lower concentration. Osmosis is the movement of water through a partially permeable membrane from a dilute solution to a more concentrated solution.
Active transport moves substances against a concentration gradient and requires energy from respiration.
Key points: A steeper concentration gradient usually increases diffusion rate.; Higher temperature gives particles more kinetic energy.; A larger surface area can increase the rate of exchange.
#### Microscopy and magnification
Use magnification = image size ÷ actual size. Keep units consistent before calculating, and convert millimetres to micrometres when needed. Show the conversion step so your method is clear.
Canonical page: https://tutorium.uk/resources/gcse-biology/cells

### GCSE Quadratic Equations Guide | Tutorium
Learn how to solve GCSE quadratic equations by factorising, using the quadratic formula and checking solutions.
Level: GCSE Maths; subject: Maths; topic: Quadratic equations
#### Factorising simple quadratics
For x² + bx + c = 0, find two numbers that multiply to c and add to b. Write the expression as two brackets, set each bracket equal to zero, and solve both linear equations.
For example, x² + 5x + 6 = 0 becomes (x + 2)(x + 3) = 0, so x = −2 or x = −3.
#### The quadratic formula
For ax² + bx + c = 0, use x = (−b ± √(b² − 4ac)) ÷ 2a. Substitute a, b and c with their signs in brackets, and keep the plus-or-minus symbol until you calculate both answers.
The expression b² − 4ac is the discriminant. It helps indicate whether the equation has two, one or no real solutions.
#### Checking and presenting answers
Substitute each solution back into the original equation. If the question comes from a length, area or time problem, reject any solution that does not make sense in context and state the units where appropriate.
Canonical page: https://tutorium.uk/resources/gcse-maths/quadratic-equations

### GCSE English Language Analysis Guide | Tutorium
A practical GCSE English Language guide to analysing quotations, methods, effects and writer's choices.
Level: GCSE English Language; subject: English; topic: Language analysis
#### A focused analysis paragraph
Start with a clear point that answers the question. Embed a short quotation, zoom in on one or two words, and explain the connotations or associations created for the reader.
Finish by linking the effect to the character, situation or writer's purpose. Keep the explanation anchored to the exact wording rather than retelling the plot.
Key points: Point: what does the writer show?; Evidence: which short quotation proves it?; Analysis: what does a key word suggest?; Purpose: why might the writer want the reader to think or feel this?
#### Methods worth identifying
You may analyse a metaphor, simile, personification, contrast, semantic field, adjective, verb, sentence type or sound pattern. Naming a method is useful only when it supports an explanation of the quotation's meaning and effect.
For example, a verb can reveal movement or intention, while a semantic field can build a sustained atmosphere across several words.
#### Improve precision
Replace general comments such as 'this makes the reader want to read on' with a specific response. Explain whether the reader feels uneasy, sympathetic, curious or shocked, and identify the word or image that creates that response.
Canonical page: https://tutorium.uk/resources/gcse-english/language-analysis

### GCSE Simultaneous Equations Guide | Tutorium
A clear GCSE Maths guide to solving simultaneous equations by elimination, substitution and checking the intersection.
Level: GCSE Maths; subject: Maths; topic: Simultaneous equations
#### What a simultaneous solution means
A pair of linear equations has a simultaneous solution when one pair of values makes both equations true. On a graph, the solution is the point where the two straight lines meet.
Write the equations clearly before choosing a method. Look for matching or easily matched coefficients when elimination is likely to be efficient.
Key points: The solution is an ordered pair such as (x, y).; Substitute the values into both original equations when checking.; Keep negative signs attached to the term they belong to.
#### Elimination and substitution
For elimination, add or subtract the equations so that one variable disappears, then solve the remaining equation. If the coefficients do not match, multiply one or both equations first.
For substitution, rearrange one equation to make a variable the subject, substitute it into the other equation, and solve. Substitute the answer back to find the second variable.
#### Check the pair, not just the algebra
A quick check is to put both values into each original equation. In a word problem, explain what each value represents and reject a value that is impossible for the context, such as a negative length.
Canonical page: https://tutorium.uk/resources/gcse-maths/simultaneous-equations

### GCSE Electricity Explained | Tutorium
A GCSE Physics guide to current, charge, potential difference, resistance, circuit equations and series and parallel circuits.
Level: GCSE Physics; subject: Physics; topic: Electricity
#### Current, charge and time
Current is the rate of flow of charge. Use Q = I t, where charge is measured in coulombs, current in amperes and time in seconds. Rearrange the equation only after identifying the quantity required.
In a series circuit the current is the same at every point. In a parallel circuit the current splits between branches and the total current is the sum of the branch currents.
Key points: Q = I t; Charge is measured in coulombs (C).; Current is measured in amperes (A).
#### Potential difference and resistance
Potential difference measures the energy transferred per unit charge. Resistance describes how strongly a component opposes current. Use V = I R, with voltage in volts, current in amperes and resistance in ohms.
In series, potential differences add and the total resistance is the sum of the component resistances. In parallel, the potential difference is the same across each branch and the total resistance is lower than the resistance of the smallest branch.
#### A safe exam method
Label the values on the circuit, identify whether it is series or parallel, and write the equation before substituting. Check that the unit in the final answer matches the quantity asked for and use the component graph if the resistance changes with temperature or light.
Canonical page: https://tutorium.uk/resources/gcse-physics/electricity

### GCSE Genetics and Inheritance Guide | Tutorium
Understand GCSE Biology DNA, genes, chromosomes, alleles, genetic diagrams, variation and inheritance.
Level: GCSE Biology; subject: Biology; topic: Genetics and inheritance
#### DNA, genes and chromosomes
A gene is a section of DNA that contains instructions for a characteristic, often by coding for a protein. Chromosomes are long DNA molecules found in the nucleus, and body cells contain pairs of chromosomes.
Different versions of a gene are called alleles. A person's combination of alleles contributes to their genotype, while the observable characteristic is the phenotype.
Key points: DNA contains genetic information.; A gene is a section of DNA.; Alleles are different versions of a gene.; Phenotype is the observed characteristic.
#### Using genetic diagrams
Write the parent genotypes, list the possible gametes, then combine one gamete from each parent in a Punnett square. State the possible genotypes and phenotypes and give probabilities as fractions, decimals or percentages when asked.
A dominant allele is expressed when at least one copy is present. A recessive characteristic is expressed only when the individual has two copies of the recessive allele.
#### Variation and selection
Variation can be genetic, environmental or a combination of both. Mutations create new alleles, and natural selection can change the frequency of characteristics in a population over generations. Use the stages in order and avoid saying that an individual changes because it needs to.
Canonical page: https://tutorium.uk/resources/gcse-biology/genetics

### GCSE Unseen Poetry Guide | Tutorium
A practical GCSE English guide to approaching unseen poetry, analysing language and structure, and comparing poems precisely.
Level: GCSE English Literature; subject: English; topic: Unseen poetry
#### Read for the whole movement
Read the poem once for its overall situation and again to mark changes in voice, setting, mood or focus. Notice the title, opening, ending and any repeated words or images before choosing quotations.
Turn the question into a clear argument. If it asks how a relationship changes, track that change across the poem instead of analysing isolated lines.
Key points: Start with the question and the poem's overall idea.; Mark a shift in tone, speaker, time or setting.; Use short quotations that are easy to analyse closely.
#### Language, structure and form
Zoom in on a precise word or image and explain its connotations. Then consider how the line, stanza, sentence or sound pattern shapes the reader's experience. A technique label only helps when it leads to a specific interpretation.
The ending can echo, challenge or resolve an earlier idea. Use that relationship as evidence for a thoughtful interpretation rather than treating the final line as a separate point.
#### Comparing two poems
Make the comparison part of every paragraph. State what the poems share or how they differ, use a short quotation from each, and explain why the poets' choices create different effects. Keep the comparison focused on the question.
Canonical page: https://tutorium.uk/resources/gcse-english/unseen-poetry

### A-Level Chemical Equilibria Guide | Tutorium
A concise A-level Chemistry guide to dynamic equilibrium, Le Chatelier's principle, equilibrium constants and exam reasoning.
Level: A-level Chemistry; subject: Chemistry; topic: Chemical equilibria
#### Dynamic equilibrium
In a closed system, a reversible reaction can reach dynamic equilibrium. The concentrations of reactants and products remain constant because the forward and reverse reaction rates are equal, even though particles continue to react.
The equilibrium position describes the relative amounts of reactants and products at equilibrium. It is not the same as the reaction rate.
Key points: The system must be closed for the usual equilibrium model.; Forward and reverse reactions continue.; Equal rates do not mean equal concentrations.
#### Predicting a change
Le Chatelier's principle says that a system responds to a change in conditions in the direction that opposes that change. For a temperature change, treat heat as a reactant or product depending on whether the forward reaction is endothermic or exothermic.
Changing pressure affects a gaseous equilibrium when the two sides have different total numbers of gas molecules. A catalyst increases both rates and does not change the equilibrium position.
#### Equilibrium constants
The expression for Kc depends on the balanced equation and the convention in the relevant specification. Write the powers from the stoichiometric coefficients, omit pure solids and liquids where appropriate, and include units only when the question or specification requires them.
Canonical page: https://tutorium.uk/resources/a-level-chemistry/equilibria

### A-Level Differentiation Guide | Tutorium
An A-level Maths guide to differentiating powers, finding gradients, stationary points and interpreting derivatives.
Level: A-level Maths; subject: Maths; topic: Differentiation
#### The power rule
For a term ax^n, differentiate by multiplying by n and reducing the power by one: d(ax^n)/dx = anx^(n-1). Constants differentiate to zero because they do not change as x changes.
Differentiate each term separately, keep brackets organised and simplify only after applying the rule.
Key points: The derivative gives the gradient function.; A constant has derivative zero.; Check the power and coefficient after each term.
#### Stationary points
A stationary point occurs where the gradient is zero, so solve f'(x) = 0 and substitute the x-values into the original function to find coordinates. The second derivative can help classify a local maximum or minimum when the method is allowed.
A derivative can also be used to find where a function is increasing or decreasing by studying the sign of f'(x).
#### Interpret the result
Write a conclusion in the language of the question. A gradient may represent a rate of change, while a stationary point may represent a turning point or an optimum. Include coordinates and units where they are relevant.
Canonical page: https://tutorium.uk/resources/a-level-maths/differentiation

### GCSE Chemical Bonding Guide | Tutorium
Understand GCSE Chemistry ionic, covalent and metallic bonding, structure, properties and exam explanations.
Level: GCSE Chemistry; subject: Chemistry; topic: Chemical bonding
#### Ionic bonding
Ionic bonding forms when electrons transfer from one atom to another, creating positive and negative ions. The ions are held in a giant lattice by strong electrostatic attractions between opposite charges.
Ionic compounds have high melting points because many strong attractions must be overcome. They conduct electricity when molten or dissolved because the ions can move, but not when solid because the ions are fixed in place.
Key points: Metals usually form positive ions by losing electrons.; Non-metals usually form negative ions by gaining electrons.; The formula must balance the total positive and negative charge.
#### Covalent and metallic structures
Covalent bonding is the sharing of pairs of electrons between non-metal atoms. Simple molecules have strong bonds within each molecule but weaker intermolecular forces between molecules; giant covalent structures have bonds throughout a large lattice.
Metallic bonding consists of positive metal ions surrounded by delocalised electrons. The mobile electrons explain why metals conduct electricity, while layers of ions can slide so metals are malleable.
#### Link structure to properties
A strong answer names the structure, identifies the force or particle that matters and then links it to the property. Avoid saying that a substance is strong or conductive without explaining what moves or what must be overcome.
Canonical page: https://tutorium.uk/resources/gcse-chemistry/bonding

### GCSE Energy Stores and Transfers Guide | Tutorium
A GCSE Physics guide to energy stores, transfers, efficiency, power and calculating energy in everyday systems.
Level: GCSE Physics; subject: Physics; topic: Energy
#### Stores and pathways
Common energy stores include kinetic, gravitational potential, elastic, thermal, chemical and magnetic stores. Energy can be transferred mechanically, electrically, by heating or by radiation such as light or sound.
In a real device some energy is dissipated to the thermal store of the surroundings. Dissipated energy has not disappeared; it has spread to less useful places.
Key points: Kinetic energy depends on mass and speed.; Gravitational potential energy depends on mass, gravitational field strength and height.; Power is the rate of energy transfer.
#### Useful equations
Use kinetic energy = 0.5 x mass x speed^2 and gravitational potential energy = mass x gravitational field strength x height. For power, use power = energy transferred / time or power = work done / time.
Efficiency compares useful output to total input. Write it as a decimal or multiply by 100 for a percentage, following the form requested by the question.
#### Explain efficiency clearly
When a question asks why a device is not 100 percent efficient, identify the unwanted transfer, such as heating due to friction or electrical resistance, and say where the energy goes. Do not describe energy as being destroyed.
Canonical page: https://tutorium.uk/resources/gcse-physics/energy

### GCSE Respiration Guide | Tutorium
Learn GCSE Biology aerobic and anaerobic respiration, equations, exercise responses and required practical links.
Level: GCSE Biology; subject: Biology; topic: Respiration
#### Aerobic respiration
Aerobic respiration uses glucose and oxygen to release energy, producing carbon dioxide and water. It takes place in mitochondria and supplies energy for active transport, muscle contraction and other cell processes.
The energy is transferred rather than created. A useful equation is energy transferred = power x time when a question describes a device or process using the energy.
Key points: Word equation: glucose + oxygen -> carbon dioxide + water.; Aerobic respiration releases more energy than anaerobic respiration.; It happens continuously in living cells, not only during exercise.
#### Anaerobic respiration
When muscles cannot receive enough oxygen during vigorous exercise, anaerobic respiration releases energy from glucose without oxygen. In animal cells it produces lactic acid, which can contribute to fatigue and creates an oxygen debt that must be repaid after exercise.
In plants and microorganisms, anaerobic respiration can produce ethanol and carbon dioxide. Use the organism named in the question before writing the products.
#### Exercise and recovery
During exercise, heart rate, breathing rate and breath volume increase so more oxygen and glucose reach muscles and carbon dioxide is removed. After exercise, continued deeper breathing supplies oxygen for breaking down lactic acid.
Canonical page: https://tutorium.uk/resources/gcse-biology/respiration

### GCSE Trigonometry Guide | Tutorium
A GCSE Maths guide to right-angled triangle trigonometry, SOHCAHTOA, bearings and checking answers.
Level: GCSE Maths; subject: Maths; topic: Trigonometry
#### Choose the ratio
Relative to the chosen angle, the hypotenuse is opposite the right angle, the opposite side is across from the angle and the adjacent side touches the angle without being the hypotenuse. SOHCAHTOA links sine, cosine and tangent to these sides.
Use sine for opposite and hypotenuse, cosine for adjacent and hypotenuse, and tangent for opposite and adjacent. Write the ratio before substituting values.
Key points: Sine = opposite / hypotenuse.; Cosine = adjacent / hypotenuse.; Tangent = opposite / adjacent.
#### Find a side or an angle
For a missing side, substitute the angle and known side then rearrange. For a missing angle, use the inverse button on the calculator, such as sin^-1, cos^-1 or tan^-1. Round only at the end unless the question says otherwise.
Draw or mark the right angle and check that the side you call the hypotenuse is the longest side.
#### Apply the result to a problem
In bearings, measure clockwise from north and write three figures, such as 035 degrees. In a word problem, state what the calculated length or angle represents and include units where appropriate.
Canonical page: https://tutorium.uk/resources/gcse-maths/trigonometry

### GCSE Percentages Guide | Tutorium
A GCSE Maths guide to percentage change, reverse percentages, repeated change and checking sensible answers.
Level: GCSE Maths; subject: Maths; topic: Percentages
#### Multipliers
An increase of p percent uses the multiplier 1 + p/100. A decrease of p percent uses 1 - p/100. Multiply the original amount by the multiplier and keep the units in the final answer.
For example, a 15 percent increase uses 1.15, while a 15 percent decrease uses 0.85.
Key points: 10 percent = 0.10 as a decimal.; Increase by 25 percent: multiply by 1.25.; Decrease by 25 percent: multiply by 0.75.
#### Reverse percentages
If a final value is known after a percentage change, divide by the multiplier to find the original. Do not subtract the percentage from the final value, because the percentage was calculated from the original amount.
For repeated changes, apply each multiplier in sequence. A 10 percent increase followed by a 10 percent decrease does not return to the starting value.
#### Check the context
Estimate the result before calculating. A discount should reduce the price, a growth multiplier should be greater than one and a probability or proportion should stay within the range the question allows.
Canonical page: https://tutorium.uk/resources/gcse-maths/percentages

### GCSE Creative Writing Guide | Tutorium
A practical GCSE English guide to planning creative writing, using precise description, structure and accurate sentences.
Level: GCSE English Language; subject: English; topic: Creative writing
#### Plan a manageable story
Choose a main character, a specific setting and one change or problem. A short time span can still create tension if the character wants something, notices a threat or must make a decision.
Sketch the beginning, a shift in the middle and an ending that changes the reader's understanding. Avoid introducing too many characters or locations to fit the time available.
Key points: Give the reader a clear viewpoint.; Use a change in mood, knowledge or action to shape the structure.; Make the ending feel connected to an earlier detail.
#### Use precise description
Select details that reveal the setting or character rather than listing everything you can see. Specific verbs, sensory images and deliberate sentence lengths can create pace, atmosphere and emphasis.
Figurative language is most useful when it makes an idea clearer or more memorable. Do not force a technique into every sentence.
#### Edit for accuracy
Leave time to check paragraphs, sentence boundaries, apostrophes, homophones and verb tenses. Read the opening and ending again to make sure the voice and tense remain controlled.
Canonical page: https://tutorium.uk/resources/gcse-english/creative-writing

### A-Level Integration Guide | Tutorium
An A-level Maths guide to integrating powers, finding constants, areas under curves and interpreting results.
Level: A-level Maths; subject: Maths; topic: Integration
#### The reverse power rule
For a term ax^n, integrate by increasing the power by one and dividing by the new power: integral ax^n dx = ax^(n+1)/(n+1) + C, provided n is not -1. Integrate each term separately.
The constant C represents the family of antiderivatives. Include it for an indefinite integral and use a known point to find its value when required.
Key points: Increase the power by one.; Divide by the new power.; Add C for an indefinite integral.
#### Definite integrals and area
For a definite integral, substitute the upper and lower limits into an antiderivative and subtract lower from upper. The result is a signed area; if the graph is below the axis, use the context to decide whether a positive geometric area is required.
Sketch the curve or inspect its sign before interpreting the answer. Split the interval if the curve crosses the axis and the question asks for total area.
#### Connect derivative and integral
A derivative can describe a rate, while an integral accumulates that rate over an interval. State what the value means in the problem and keep units consistent, especially when finding displacement from velocity.
Canonical page: https://tutorium.uk/resources/a-level-maths/integration

### A-Level Mechanics Guide | Tutorium
An A-level Physics guide to motion, forces, momentum, work and modelling assumptions in mechanics problems.
Level: A-level Physics; subject: Physics; topic: Mechanics
#### Describe motion with vectors
Displacement, velocity and acceleration have direction as well as size. Choose a sign convention and keep it throughout the calculation. SUVAT equations apply to constant acceleration, so state or check that assumption before using them.
A velocity-time graph gives displacement from the area under the graph and acceleration from its gradient.
Key points: Distance and speed are scalars.; Displacement, velocity and acceleration are vectors.; Use consistent units such as metres, seconds and metres per second.
#### Forces and momentum
Use the resultant force in F = ma and show the forces on a free-body diagram. Momentum is mass x velocity, and in an isolated system total momentum is conserved before and after an interaction.
Impulse equals change in momentum. Include direction when comparing velocities before and after a collision.
#### Explain the model
If a question says to ignore air resistance, treat it as a modelling assumption rather than a fact about the real world. Explain how friction, string mass, pulley size or a non-uniform field would change the model when evaluation is requested.
Canonical page: https://tutorium.uk/resources/a-level-physics/mechanics

## Free learning tools

### GCSE revision planner
A free browser-based planner for choosing GCSE subjects, setting weekly hours and building a practical revision rhythm.
Canonical page: https://tutorium.uk/gcse-revision-planner

### Tutor match brief builder
A free browser-based tool for turning a learner’s subject, level, goal and practical details into a clear, shareable tutor request.
Canonical page: https://tutorium.uk/tutor-match-brief

### Tutor profile preview
A free browser-based tool for tutors to draft a learner-facing profile preview before applying. It does not publish a profile or expose contact details, addresses or private verification documents.
Canonical page: https://tutorium.uk/tutor-profile-preview

### Become a Tutorium tutor
Tutorium welcomes independent tutors who can provide a clear subject offer, useful learner-facing profile details and the evidence requested for review. Tutors choose their own Tutor Fee and lesson format; approval is not employment or a guarantee of work.
Canonical page: https://tutorium.uk/become-a-tutor

### How to become an online tutor in the UK
A practical checklist covering subject fit, learner-facing profile details, requested DBS and qualification evidence, online lesson setup and keeping an approved profile current. Tutorium reviews the evidence requested for an adult tutor application before a public profile is intended to be published.
Canonical page: https://tutorium.uk/blog/how-to-become-an-online-tutor-uk

### How to choose an online tutoring platform in the UK
A neutral comparison checklist covering learning goals, tutor fit, evidence and trust signals, lesson quality, total pricing, cancellation support, safeguarding, privacy and responsible use of AI assistants.
Canonical page: https://tutorium.uk/blog/how-to-choose-online-tutoring-platform-uk

### Tutor referral message builder
A free browser-based tool for creating a privacy-safe invitation for a tutor. It does not send or store the message; referrals do not bypass DBS and qualification review.
Canonical page: https://tutorium.uk/refer-a-tutor

### School tutoring pilot brief builder
A free browser-based tool for outlining a school tutoring conversation at cohort level. It does not upload form values and should not contain learner names or sensitive data.
Canonical page: https://tutorium.uk/school-pilot-brief

### Public API for AI agents
Human-readable documentation for Tutorium's read-only tutor and subject API, discovery manifests, AI Catalog entry and safety boundaries. Agents can discover published information but cannot book, message or expose private documents.
Canonical page: https://tutorium.uk/for-ai-agents

### Press and partner information
A factual, citable overview of Tutorium, its independent-tutor model, approval language, responsible claims and canonical source links for media, researchers and education partners.
Canonical page: https://tutorium.uk/press
Machine-readable kit: https://tutorium.uk/press-kit.json
Partner link kit: https://tutorium.uk/press#partner-link-kit
Partner badge: https://tutorium.uk/tutorium-partner-badge.svg

## High-intent service guides

### Online tutoring that fits around real life.
Find approved online tutors across the UK for Maths, English, Science and more. Compare profiles, request focused lessons and keep learning organised with Tutorium.
Audience: For school learners, parents, adult learners and anyone who wants flexible one-to-one or group learning support.
#### What can online tutoring help with?
Online tutoring is useful when a learner needs a calm explanation, regular accountability or targeted practice rather than another generic worksheet. A tutor can work through a difficult topic, model a method, review an answer and adapt the next lesson around what the learner has understood.
Tutorium supports subject-focused learning for school and adult learners. The most useful starting point is a specific goal: a GCSE topic, an upcoming assessment, confidence with a skill, a qualification, or a longer-term study plan.
Key points: Maths, English and science support from primary through GCSE and A-level; Revision planning, exam-question practice and feedback on technique; Adult learning for qualifications, career development or personal goals; Online one-to-one lessons, with group options where a published lesson supports them
#### How Tutorium keeps online lessons focused
The platform is designed around a simple sequence. Start by comparing published tutor information. Use the available communication route to ask about fit, syllabus and goals. Request a suitable time and lesson length, then keep the confirmed details and follow-up information together.
Tutorium also provides learning resources and an integrated online classroom experience. Those tools are there to support human teaching, not to replace the tutor's judgement or promise a particular grade.
Key points: Choose a subject and level before you compare profiles; Ask about the exact syllabus, exam board and learning goal; Confirm the delivery mode, price and timing before the lesson; Use safeguarding and support routes promptly if a concern arises
#### How to choose an online tutor
The best profile is not always the longest or most expensive. Look for a clear match between the tutor's published subject experience and the learner's current need. A short message about the topic, level, preferred pace and intended outcome will usually reveal more than a broad request for help.
Parents and adult customers should remain in control of the account and booking decisions. Read the tutor's profile and the trust information, ask sensible questions, and make sure the planned lesson is appropriate before confirming it.
Canonical page: https://tutorium.uk/online-tutoring

### GCSE tutoring built around the gaps that matter.
Find approved GCSE tutors for Maths, English, Biology, Chemistry, Physics and Combined Science. Compare level support, exam-board fit and online lesson options on Tutorium.
Audience: For GCSE learners, parents and guardians, home educators and adult learners revisiting GCSE-level subjects.
#### What GCSE tutoring should cover
Effective GCSE support is more specific than 'revise harder'. A learner may need a concept explained from first principles, a set of mistakes diagnosed, help planning a long answer, or practice applying knowledge under time pressure. A good first lesson makes that need clearer.
Tutorium's subject pages outline common GCSE levels, exam boards and topics so families can arrive at a tutor conversation with a useful starting point.
Key points: GCSE Maths: algebra, number, geometry, statistics and problem solving; GCSE English: language analysis, creative writing, reading and literature essays; GCSE Biology, Chemistry and Physics: concepts, calculations, practical skills and exam questions; Combined Science: coordinated support across the relevant biology, chemistry and physics topics
#### A practical GCSE tutoring plan
Begin by identifying the next meaningful outcome, such as understanding a topic, improving a question type or preparing for a mock. Share the specification or exam board, the learner's current confidence and any teacher feedback. The tutor can then balance explanation, worked examples, independent attempts and review.
Regular sessions are most useful when they create a loop: the learner tries a method, receives precise feedback, practises it again and records what to revisit. Parents can support the routine without taking over the teaching.
Key points: Set one or two priorities for each lesson; Keep a short record of errors and questions to revisit; Mix recall, application and exam technique; Increase timed practice gradually rather than starting with full papers
#### Choosing a GCSE tutor online or in person
Compare the tutor's published subjects, levels, experience, delivery mode and rate. Then ask the questions that matter for your learner: which specification do they know, how do they explain difficult ideas, how do they give feedback, and what would they do in the first few lessons?
Tutorium's public approval signal is one part of that decision. It does not guarantee a grade or remove the need to check that the teaching relationship is a good fit.
Canonical page: https://tutorium.uk/gcse-tutors

### Choose a tutor with confidence, not guesswork.
A practical guide to choosing a tutor in the UK: define the learning goal, check subject and level fit, ask better questions and review the first lesson.
Audience: For parents, guardians, adult learners and anyone comparing online or in-person tutoring in the UK.
#### 1. Define what the learner needs next
Begin with the next meaningful outcome rather than a vague promise to improve. That might be understanding quadratic equations, writing a stronger English analysis, preparing for a mock, rebuilding confidence after a difficult term or working towards an adult qualification.
The goal can change once a tutor understands the starting point. It is still useful to write down the current level, the topic that feels difficult, the next assessment and what the learner would like to do more confidently. Tutorium’s free tutor match brief builder turns those details into a short message you can share.
Key points: Subject, level and exam board or specification where relevant; One or two topics, skills or question types that need attention; The next assessment, qualification or practical milestone; Preferred pace, lesson format and likely weekly rhythm
#### 2. Check subject, level and teaching fit
A tutor who knows a subject is not automatically the best fit for every level or goal. Read the published profile for the exact subject, qualification and learner stage. For GCSE and A-level work, ask the tutor to confirm current experience with the relevant exam board and specification before requesting a lesson.
Teaching fit matters as much as subject knowledge. Ask whether the tutor uses worked examples, retrieval practice, exam questions, discussion, visual explanations or another approach that suits the learner. A clear answer is more useful than a generic claim that every learner is different.
Key points: Published subject and level experience that matches the learner; A teaching approach the learner can understand and participate in; Online or in-person delivery that works for the household; Availability, lesson length and rate that fit the plan
#### 3. Check safety and approval information
For tuition involving children or young people, adults should read the platform’s safeguarding information and keep the account and booking decisions under appropriate adult control. Tutorium reviews the evidence behind tutor applications, including DBS evidence and qualification certificates, before a profile is intended to appear publicly. The public approval indicator is a summary, not a reason to stop asking sensible questions.
Do not ask a public profile or an agent to reveal private certificates, addresses or account information. Use the platform’s reporting and support routes if something feels unsafe, and keep practical lesson communication where it can be handled responsibly.
Key points: Read the current trust and safeguarding pages; Check the public approval indicator and the tutor’s published details; Keep private documents and personal information private; Agree who controls the account and lesson request before booking
#### 4. Ask questions that reveal the first step
A useful first message gives the tutor enough context to respond specifically. Ask what they would want to know before the first lesson, how they would diagnose the gap and what a realistic first milestone could be. You are not trying to design a whole course in one message; you are checking whether the tutor can turn the learner’s situation into a sensible next action.
After the first lesson, review what became clearer, what the learner attempted independently and what should happen next. If the explanation, pace or working relationship is not right, say so early and use the brief to compare another option.
Key points: What would you cover in the first lesson?; How would you find out what the learner already understands?; How do you use practice questions and feedback?; What should the learner do between lessons?
Canonical page: https://tutorium.uk/how-to-choose-a-tutor

### Compare tutoring costs with the full picture in view.
Understand what affects tutoring prices in the UK, how to compare lesson costs fairly and what to ask before choosing an online or in-person tutor.
Audience: For parents, guardians, adult learners and anyone comparing online or in-person tutoring costs in the UK.
#### What affects a tutor's price?
Tutors set their rates around the service they offer and the learners they support. Subject and level matter: a specialist lesson for a particular qualification may involve different preparation from a general confidence-building session. Experience, teaching approach and demand can also affect the published rate.
The lesson format changes the practical picture too. Online lessons may avoid travel, while in-person lessons may include a local service area or travel time. A group lesson can have a different price structure from one-to-one tuition. Read the profile and confirm the exact lesson details rather than assuming that one price describes every option.
Key points: Subject, qualification and learner level; Tutor experience and specialist preparation; Online, in-person or group delivery; Lesson length, frequency and local travel arrangements; The platform total and any clearly shown service charges
#### How to compare rates fairly
Start by writing down the outcome you are paying for: a weekly GCSE Maths routine, an A-level topic, exam-question feedback, adult qualification support or something else. Then compare tutors who publish a similar subject and level fit. Ask what a first lesson includes, how the tutor gives feedback and what preparation is expected between sessions.
Do not compare a short introductory conversation with a full lesson, or an in-person quote with an online quote, without checking what is included. Before confirming a request, review the lesson length, delivery mode, rate, cancellation terms and the total displayed by Tutorium.
Key points: Use the same subject, level and goal when comparing profiles; Check whether the displayed rate is hourly and which lesson length applies; Ask whether preparation, resources or travel arrangements change the price; Confirm the full total and cancellation terms before requesting a lesson
#### Choose value, not just the lowest number
A lesson is more likely to feel worthwhile when it gives the learner a clear explanation, a chance to practise and a next step they can repeat independently. A tutor who understands the learner's level and can explain their approach may be a better fit than a cheaper option that does not match the goal.
Use Tutorium's approval and safeguarding information as part of a wider decision. It is sensible to compare the public profile, ask focused questions and start with a clearly defined first milestone. The cheapest advertised rate should never override safety, subject fit or an adult customer's control of the account.
#### Set a realistic tutoring budget
Choose a weekly or monthly limit before you contact a tutor, then decide how often the learner genuinely needs support. A focused session every week may be more useful than an irregular burst of lessons that is difficult to sustain. If the goal changes, revisit the frequency and the type of support rather than treating the first plan as permanent.
Tutorium's free tutor match brief builder lets you share a subject, level, goal, preferred format, rhythm, budget guide and availability without creating an account. It gives a tutor enough context to respond clearly while leaving the final price and lesson arrangement for the normal confirmation process.
Key points: Set a maximum you can sustain rather than a one-off stretch budget; Decide whether weekly, twice-weekly or targeted sessions fit the goal; Leave room for the plan to change after the first lesson; Write the budget guide into the first message so expectations are clear
Canonical page: https://tutorium.uk/tutor-cost-uk

### A-level support for deeper thinking and better questions.
Find approved A-level tutors for Maths, English, Biology, Chemistry and Physics. Compare subject fit, exam-board experience and lesson options with Tutorium.
Audience: For sixth-form and college learners, parents and guardians, home educators and adults studying A-level subjects.
#### Where A-level tutoring adds value
A-level learners often know the basic facts but struggle to connect them, apply them in a new context or explain them with enough precision. A tutor can slow down a difficult idea, challenge an assumption, review a model answer and help the learner decide what to practise next.
Support can be occasional and targeted or part of a regular routine. The right pattern depends on the subject, timetable, confidence and upcoming assessments.
Key points: A-level Maths: algebra, functions, calculus, mechanics and statistics; A-level Chemistry: structure, energetics, rates, equilibria, organic chemistry and practical reasoning; A-level Biology: cells, genetics, physiology, ecology, homeostasis and data analysis; A-level Physics and English: concepts, extended responses, calculations, analysis and exam technique
#### A-level exam preparation without last-minute cramming
Start with the specification and a realistic picture of what is secure, uncertain and unfamiliar. Use tutoring to target the uncertain areas, but keep independent practice between lessons. Past-paper work becomes more useful when the learner can explain why an answer lost marks and what will change next time.
For university applications or a change of direction, a tutor can also help a learner organise subject knowledge and communicate their reasoning. Any admissions or grade outcome remains dependent on the learner and the relevant institution.
Key points: Map topics to the current exam specification; Practise explanations as well as final answers; Review calculations, units, evidence and command words; Keep a small, prioritised list of questions between lessons
#### How to compare A-level tutors
Look for a clear subject and level match first. Then ask how the tutor approaches difficult material, how they use exam questions, whether they know the relevant exam board and what a first session would cover. A tutor's rate and availability matter, but a good academic fit matters just as much.
Tutorium provides public profile and safety information to support an informed decision. Read the profile carefully, keep expectations realistic and confirm the exact lesson details before booking.
Canonical page: https://tutorium.uk/a-level-tutors

### A clearer starting point for school tutoring partnerships.
Explore a responsible starting point for school tutoring partnerships in the UK: focused online or in-person support, tutor approval visibility and a clear pilot conversation.
Audience: For schools, multi-academy trusts, sixth forms, colleges, alternative provision and education teams exploring tutoring support.
#### What a sensible school tutoring pilot should clarify
A useful pilot is small enough to learn from. Set out which learners or cohort are in scope, which subjects and levels matter, whether lessons are online or in person, how the timetable would work and what evidence would make the next decision clearer.
The question might be academic, practical or operational: can a group access reliable GCSE Maths support, can targeted science revision fit the school day, can adult-controlled communication reduce avoidable administration, or can learners use shared resources between sessions? Keep the first question narrow enough to review honestly.
Key points: Year group, qualification, subject and broad learning need; Cohort size, lesson frequency, lesson length and delivery mode; The adult or staff roles responsible for communication and decisions; A measurable outcome and a review point rather than an open-ended promise; Accessibility, timetable, budget and practical constraints
#### Questions to cover before any school rollout
Schools and trusts should carry out their own safeguarding, data protection, accessibility, procurement and contractual checks. Tutorium's public trust and privacy pages help frame the questions, but a public website cannot approve a school's use of a tutoring service or replace the organisation's policies.
Ask how tutor evidence is reviewed, which indicators are public, how an incident would be reported, who controls an account when learners are under 18, what information must stay private, how lessons are confirmed and how a school would stop or change a pilot.
Key points: Tutor approval, DBS and qualification evidence review; Safeguarding lead, reporting route and escalation responsibilities; Data minimisation, retention, access and international-transfer questions; Adult-controlled accounts and communication boundaries; Cancellation, pricing, accessibility and service-continuity arrangements
#### A platform should support teachers, not replace them
Tutoring is most useful when a human tutor can understand the learner's starting point, explain a difficult idea, give precise feedback and adapt the next attempt. Digital tools should make that work easier to organise, not claim to guarantee a grade or remove professional judgement.
Tutorium's learning resources and classroom features are intended to sit alongside human teaching. Schools should agree what tutors may access, what staff need to see, how resources are selected and how learners are supported when the platform is not the right fit.
#### How to open the conversation
Use the free school pilot brief builder to write a cohort-level outline without adding learner names or sensitive information. Share it internally first, then decide whether to contact Tutorium with the questions your organisation needs answered.
If the initial conversation is promising, agree a written scope, named responsibilities, review criteria and a stop condition before anyone treats the idea as a programme.
Canonical page: https://tutorium.uk/for-schools

## Public tutor profiles

No public tutor profiles currently contain enough learner-facing detail for this expanded directory.